Maybe I shouldn't have started this blog now, not with everything that's been going on.

In my Trigonometry classes last Tuesday we started on the Difference of Two Angles Identities, and I also introduced the Double Angle Identities, but we only had examples on the first topic, including verification and simplification of expressions involving the difference of two angles.

For these classes, I also wrote the identities and the sample questions on the left side of the board, and concentrated on the middle and right sides of the board for providing the solutions.

This was in anticipation of the use of the same material for the succeeding class in the same room. In fact, at the start of the second class, I just gave them time to copy everything first, including the solutions to the last problems which were still written on the board.

Afterwards, I discussed those last problems first before we tackled the earlier problems.

From this experience, as well as several similar straits years before, I have not changed my opinion that writing everything on the board first before discussing is not the best way to handle lectures where the students are taught problem solving.

The students are generally unattentive, even if they are given sufficient time to copy the notes.I know that at least some of the students find the verbal explanations superfluous because they already understand the process just from the notes.

It serves the same purpose as providing the students with handouts even before the class starts, which is something I never do. They sense that they have a safety net even if they do not listen to the lecture anymore.

Lastly, today's media inundated generation probably prefer the events to unfold in front of them instead of knowing what will happen next.

Besides, this worked best in the spontaneous nature of my first lecture, where in we were stuck in one example because we had to evaluate the tangent of 90 degrees, which is undefined. An alternative solution we found was to use sine over cosine instead of tangent.

In the second lecture, even though someone suggested the same wrong solution, I did not write it on the board anymore and just told them why that method of solving would not work.

There was one problem though that had the same result in both classes. Getting the exact solution (with no decimals, all whole numbers, fractions and radicals) we got a positive number in one item. Using their calculator to check if the numeric value was correct, that answer turned out negative. I could not find out the error in our calculations even during the second class, so I gave it as an assignment where the first five people to submit papers pinpointing the mistake in our calculations would get bonuses.

Next time I plan to start the classes with a short derivation of the difference of two angles identities and the double angles identities from the sum of two angle identities.

And that's Tuesday, except for a minor Deiv rant and what's happened with the academic advising which I will save for tomorrow. In the meantime, class dismissed.